to all maths geniuses...!!!!?

1) y = 1/x

This can be written as x^(-1). Bring the exponent down as a coefficeint and subtract one to the exponent to get:

(-1)*x^(-2) which can be written as:

dy/dx = -1/(x^2)

2) y = 3/(x^2)

This can be written as 3*x^(-2). Bring the exponent down as a coefficeint and subtract one to the exponent to get:

-2*3*x^(-3) which can be written as:

dy/dx = -6/(x^3)

3) y = x^(3/4)

Bring the exponent down as a coefficeint and subtract one to the exponent to get:

(3/4)*x^(-1/4)

This can be written as:

dy/dx = 3 / (4* x^(1/4))

4) y = 1/2x

Bring the exponent down as a coefficeint and subtract one to the exponent to get:

1*(1/2)*x^0

x^0 is always = 1, so, this would be: 1*(1/2)*1

dy/dx = 1/2

5) y = 3x^4 - 1/(x^(1/2))

The first term should be the same as before, and you get 12*x^3.

The second term can be rewritten as x^(-1/2), which become: (-1/2)*x^(-3/2). This can be written as (-1 / (2x^3/2))

Then write out the equation as:

dy/dx = 12*x^3 + (1 / (2x^3/2))

6) y = 1/x + 2/(3x)

The first term is just like problem 1: -1/(x^2)

The second term can be written as 2*(3x^-1). Bring the exponent down as a coefficeint and subtract one to the exponent to get: -1*2*(3x^-2), also known as

dy/dx = -1/(x^2) - 2/(3x^2)

7) x3 – 3x2 + 5x – 12 when x = 2

Take the derivative and plug in whatever is given as x:

dy/dx = 3x^2 - 6x + 5

y'(2) = 3(2)^2 - 6(2) + 5

= 12 - 12 + 5

= 5

8) y = x^(1/2) + 2x when x = 9

The derivative is:

dy / dx = 1/(2x^(1/2)) + 2

y'(9) = 1/(2*9^(1/2)) + 2

= 1/6 + 2

= 13/6

9) 1/(x^2) - 3x^2 when x = 2

The derivative is:

-2/(x^3) - 6x

y'(2) = -2/(2^3) - 6(2)

= -2/8 - 12

= -1/4 - 12

= -49/4

You will love wolframalpha.com. It can do all that for you.

"Find the derivative of 1/x dy"

Press enter.

The gradient is the same thing as a slope.

1. Graph the equation.

2. Find the y value at the point on the graph from the given x value.

Gradient = change in y / change in x

1) y = x^-1 dy/dx = -x^-2 = -1/x^2

2) y = 3(x^-2) dy/dx = -6(x^-3) = -6/x^3

3) y = x^(3/4) dy/dx = 3/4(x^-1/4)

4) dy/dx = 1/2

5) I assume you mean: y = 3x^4 - x^-1/2 ao dy/dx = 12x^3 +1/2x^-3/2

6) dy/dx = -x^-2 + 2/3

7) dy/dx=3x^2 -6x +5 at x = 2 dy/dx = 12-12+5 = 5

8) dy/dx =1/2x^-1/2 + 2 at x=9 dy/dx = 1/6 +2 = 2 1/6

9) dy/dx = -2x^-3 -6x at x=2 dy/dx = -1/4 -12 = -12 1/4

yaw

1) derivative = -1/(x^2)

2) derivative = -6/(x^2)

3) derivative = (3/4)(x^(-1/4)) or simpler 3 divided by (4 x 4th root x)

4) derivative = -1/((2x)^2)

5) derivative = 3x^(4-(1/sqrtx)) (ln(3x)+1) *im not totally sure about this

6) derivative = -5/(3x^2)

btw for 5 i thought meant y = 3x^(4-(1/sqrt x))

unfortunaltely idk what the **** a fgradient is so good luck with that